The present invention relates generally to tunable low-impedance capacitive micromechanical resonators and oscillators and fabrication methods relating thereto.
High performance HF and VHF micromechanical resonators for frequency references and filters require low motional impedance, high quality factor, and frequency tunability. The requirements are derived from the needs for low power consumption, low phase noise, temperature compensation, and resonator array matching. It would be desirable to have micromechanical resonators with quality factors Q similar to quartz crystal units, and the like, and also addresses low impedance and tuning requirements. Typical quartz crystal units have Q of 10,000 or more and frequency variation in the range of 50 ppm over 100° C.
Conventional capacitive micromechanical resonators such as beams, disks, and blocks, each have unique features, but do not meet all the above requirements. HF and VHF capacitive beam resonators have high tunability, but typically have low Q. This is discussed by S. Lee, M. U. DeMirci and C. Nguyen, “A 10-MHz micromechanical resonator Pierce reference oscillator,” Tech. Dig. Transducers 01, pp. 1094-1098, 2001. Bulk mode disk and rectangular resonators have high Q, but suffer from poor tunability. This is discussed by S. Pourkamali, Z. Hao, and F. Ayazi, “VHF Single Crystal Silicon Capacitive Elliptic Bulk-Mode Disk Resonators,” published in JMEMS, V13 N6, 2004, and by S. Pourkamali, G. K. Ho, F. Ayazi, “Vertical Capacitive SiBARs,” published in Proc. IEEE MEMS'05, 30 Jan.-3 Feb. 2005, pp. 211-214. Therefore, a design that satisfies all the above requirements was developed and is disclosed herein.
Reference oscillators have stringent requirements on phase noise and temperature stability, which translate into resonator requirements of high quality factor and frequency tunability. Low motional impedance is also necessary to sustain oscillations and to minimize power consumption. For optimal performance, the interface circuit should include an amplifier circuit that minimizes Q loading, and a means to compensate for the frequency-temperature drift of the resonator. Temperature compensation is most easily achieved using electrical techniques, in which a controlled voltage or current provides frequency tuning. Depending on the employed tuning mechanism, the voltage necessary to properly tune the resonator frequency may not be a linear function. Therefore, it would be desirable to have a mechanism that provides for this.
The most attractive feature for micromechanical resonators is the ease with which multiple resonators can be fabricated. Pluralities of resonators at the same nominal frequency and pluralities of resonators at different target frequencies can be simultaneously fabricated. In applications where closely spaced resonator frequencies (on the order of 1% or less) are required, a robust and reliable technique to design the resonators is desirable.
A plurality of resonators can also be disposed in a coupled-resonator system to provide specific frequency characteristics. High performance bandpass filters, for example, can be constructed using resonators with low impedance, high Q, and good tunability. For this reason, the herein disclosed resonators are also desirable for coupled-resonator systems.
The absolute frequency tolerance of typical quartz crystal units is ±10 to ±50 ppm. Hence, the applicability of micromechanical resonators is contingent on a low-cost manufacturing process that meets similar performance metrics. It would be desirable to have a micromechanical resonator that may be designed for manufacturability (DFM), so that its center frequency is robust to lithography and micromachining variations.